Greytheory灰色模型.ppt
灰色理論鄧聚龍、郭洪 編著全華出版報告：王乾隆大綱灰色系統灰生成灰建模灰預測什麼是灰色-GreyTheory1982GreySystemTheory 鄧聚龍提出針對系統模型之不確定性及資訊之不完整性，進行系統的關連分析及模型建構，並藉著預測及決策的方法來探討與瞭解系統。信息不完全、不確定的系統研究少數據不確定性的學科基本原理差異信息原理：a比b高解的非唯一性原理：同一病，中、西醫不同解法最少信息原理：直線是最少資訊圖信息根據認知原理：須以資訊作為依據新息優先原理：新息的權比舊息的權大灰性不滅原理：人類認知是無窮盡的Grey、Probability、Fuzzy的區別灰生成灰色系統理論：序列的變換為序列生成；稱序列中的變換為數據生成或數據構造數據生成n數據處理，加工n數據累加，累減n數據差補或剔除n數據組合n數據映射、取代、借用 數據生成的目的n數據相對值化：初值化、平均值化、區間值化n極性變換：效果測度n層次變換：累加生成、累減生成灰生成累加生成AGO定義條件累減生成IAGO定義條件灰建模用序列建立具有部分微分方程性質的模型部分微分方程性質的模型即微分方程模型微分方程模型n只適合連續可微的對象n屬於無窮信息空間GM(1,1)定義型白化型白化響應式灰色預測-1GM(1,1):graymodelone-orderonevarianceExample:nGM(1,1)之預測方程式為：灰色預測-2建立建立GM(1,1)GM(1,1)之步驟：之步驟：輸入：一原始數據序列。輸出：GM(1,1)預測模型。步驟 1:求出累加生成序列如下：步驟 2:求出之均值序列如下：灰色預測-3步驟 3:求中間參數C,D,E,F如下：步驟 4:計算式（1）中之a、b係數如下：發展係數灰作用量灰色預測-4假設一時間序列如下所示：37471.99,37460.05,37222.60,36895.52,35734.30 灰色預測-5灰預測先建立GM（1,1）模型，依據此模型進行預測。分為：n數列灰預測n災變灰預測n季節災變灰預測以灰色預測頻率空間為基礎的影像壓縮技術GreyPredictionandFrequency-DomainBasedImageCompression作者：黃詠淮、謝明興、曾定章、莊永達2000年灰色系統理論與應用研討會報告：王乾隆Architecture Original Image DWT EZW Grey(1,1)compression compression imageHuffman codeDWT(DiscreteWaveletTransform)HL1HL2HH1LH1HH2LH2HL3HL4LL4EZW(EmbeddedZerotreeWavelet)WavelettreeEZW(EmbeddedZerotreeWavelet)Zerotree:ifallthevalueofsomeonewavelettreeelementsnomorethenthresholdT1wasgiven.Thenwecallthesub-wavelettreeiszerotree.Zerotreeimplythattheblockwassmoothlyanditisnotveryimportanttoimage.UsedGreyPredictiontoCompressionAfterDWTandEZWwehaveasequencedata.IfsomepointisnomorethenthethresholdT2,thenwemaketheGM(1,1)modelelseornot.Ifn=4wastheworstcase,butn4wasnot.nn,a,breplacethemodelsequences.ApplyZerotreetodistinguishbetweentheinsignificantandsignificantcoefficientsMorethenthresholdT1issignificantcoefficientsthatisimportantforanimage.IfnomorethenT1,itisthesmoothpartsofanimage,sowereplacethembyzerotoincreasethecompressionrate.DWT+GM(1,1)tocompressionImage-1Step1:Originalimage4levelDWTthengot13wavebands.Step2:encodingLL4byuniformquantization.均勻量化Step3:for13wavebandssetupthezerotree.nStorethesignmapofsignificantnStoretherelationbetweensignificantandinsignificantcoefficientsDWT+GM(1,1)tocompressionImage-2Step4:applytheGM(1,1)tomodelthesignificantsequences.Storethen,a,b.Step5:encodethesignificantcoefficientssignmap,uniformquantizationofLL4,allthen,a,b.Step6:decode.inversethecompressionsteps.ExperimentCR:compressionrationnCR=(bitsoftheoriginalimage)/(bitofcompressionimage)ConclusionGreymodelisgoodtohighcompressionrateSignmapproblem,storethesignmapincreasethedata.Onlyletthegreymodeltopredicttheoriginalwavelettree,dontcarethesignproblem,thenwecanraisethecompressionqualityreally.
